The language of graphs
Mathematics. 1st Year Secondary Education
You know…
 Cartesian coordinate system
x-axis: horizontal
y-axis: vertical
Origin: point (o,o)
 To plot points on a grap...
“You have to be able to understand the
qualitative meaning
of a graph”
“Let’s practice together…”
Hamilton Alonso Vettel
Podiums
World Championships
Podiums
WorldChampionships
A
H
V
“Who has more Podiums?”
“Who has won m...
Hamilton Alonso Vettel
Podiums
World Championships
Podiums
WorldChampionships
A
H
V
“Who has more Podiums?” ALONSO
“Who ha...
Hamilton Alonso Vettel
Podiums 56 95 64
World Championships 1 2 4
Podiums
WorldChampionships
A
H
V
“Who has more Podiums?”...
1. The Bus Stop Queue
Point 7 represents…
1. The Bus Stop Queue
Point 7 represents Gavin
“He is the shortest and youngest person”
7
1. The Bus Stop Queue
Point 6 represents…
7
1. The Bus Stop Queue
Point 6 represents Cathy
“She is taller than Gavin but shorter than the rest of
the people”
7
6
1. The Bus Stop Queue
Points 2 and 5 represent…
7
6
1. The Bus Stop Queue
Points 2 and 5 represent Alice or Errol
“They are the tallest”
Point 2 represents…
7
6
1. The Bus Stop Queue
Points 2 and 5 represent Alice or Errol
“They are the tallest”
Point 2 represents Alice
“She is one ...
1. The Bus Stop Queue
Points 2 and 5 represent Alice or Errol
“They are the tallest”
Point 2 represents Alice
“She is one ...
1. The Bus Stop Queue
Point 3 represents…
7
62 5
1. The Bus Stop Queue
Point 3 represents Freda
“She is shorter than Alice and Errol but taller than
the rest of the people...
1. The Bus Stop Queue
Points 1 and 4 represent…
7
62 5 2
1. The Bus Stop Queue
Points 1 and 4 represent Brendaor Dennis
“They have the same height”
Point 1 represents…
7
62 5 2
1. The Bus Stop Queue
Points 1 and 4 represent Brenda or Dennis
“They have the same height”
Point 1 represents Dennis
“He ...
1. The Bus Stop Queue
Points 1 and 4 represent Brenda or Dennis
“They have the same height”
Point 1 represents Dennis
“He ...
1. The Bus Stop Queue
7
62 5 214
2. Planes
A (Dusty) B (Siddeley)
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive than airplane A
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The...
2. Planes
A (Dusty) B (Siddeley)
3. Which Graph?
The 100 metres race.
The men's world record is
9.58 seconds, set by Usain Bolt
0,00
2,00
4,00
6,00
8,00
10...
0,00
2,00
4,00
6,00
8,00
10,00
12,00
0 20 40 60 80 100 120 140
SPEED
DISTANCE
GRAPH 3
3. Which Graph?
To sum up…
Graphsare very useful to draw conclusionsfrom different set of data
and to find if there is a correlation betwe...
The language of graphs
Mathematics. 1st Year Secondary Education
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The language of Graphs - Presentation

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El lenguage de gráficos, presentación para alumnos de primer curso de la ESO. The language of graphs presentation for students of the first year.

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  1. 1. The language of graphs Mathematics. 1st Year Secondary Education
  2. 2. You know…  Cartesian coordinate system x-axis: horizontal y-axis: vertical Origin: point (o,o)  To plot points on a graph P (3,5): “ordered pair” (3 units to the right, and 5 units up)  To plot the graph of a function y = 2x + 1
  3. 3. “You have to be able to understand the qualitative meaning of a graph” “Let’s practice together…”
  4. 4. Hamilton Alonso Vettel Podiums World Championships Podiums WorldChampionships A H V “Who has more Podiums?” “Who has won more World Championships?” H: Hamilton A: Alonso V: Vettel
  5. 5. Hamilton Alonso Vettel Podiums World Championships Podiums WorldChampionships A H V “Who has more Podiums?” ALONSO “Who has won more World Championships?” VETTEL H: Hamilton A: Alonso V: Vettel
  6. 6. Hamilton Alonso Vettel Podiums 56 95 64 World Championships 1 2 4 Podiums WorldChampionships A H V “Who has more Podiums?” ALONSO “Who has won more World Championships?” VETTEL H: Hamilton A: Alonso V: Vettel
  7. 7. 1. The Bus Stop Queue Point 7 represents…
  8. 8. 1. The Bus Stop Queue Point 7 represents Gavin “He is the shortest and youngest person” 7
  9. 9. 1. The Bus Stop Queue Point 6 represents… 7
  10. 10. 1. The Bus Stop Queue Point 6 represents Cathy “She is taller than Gavin but shorter than the rest of the people” 7 6
  11. 11. 1. The Bus Stop Queue Points 2 and 5 represent… 7 6
  12. 12. 1. The Bus Stop Queue Points 2 and 5 represent Alice or Errol “They are the tallest” Point 2 represents… 7 6
  13. 13. 1. The Bus Stop Queue Points 2 and 5 represent Alice or Errol “They are the tallest” Point 2 represents Alice “She is one of the tallest and older than Errol” So point 5 represents… 7 62
  14. 14. 1. The Bus Stop Queue Points 2 and 5 represent Alice or Errol “They are the tallest” Point 2 represents Alice “She is one of the tallest and older than Errol” So point 5 represents Errol “He is one of the tallest and younger than Alice” 7 62 5
  15. 15. 1. The Bus Stop Queue Point 3 represents… 7 62 5
  16. 16. 1. The Bus Stop Queue Point 3 represents Freda “She is shorter than Alice and Errol but taller than the rest of the people” 7 62 25
  17. 17. 1. The Bus Stop Queue Points 1 and 4 represent… 7 62 5 2
  18. 18. 1. The Bus Stop Queue Points 1 and 4 represent Brendaor Dennis “They have the same height” Point 1 represents… 7 62 5 2
  19. 19. 1. The Bus Stop Queue Points 1 and 4 represent Brenda or Dennis “They have the same height” Point 1 represents Dennis “He is older than Brenda” So point 4 represents… 7 62 5 21
  20. 20. 1. The Bus Stop Queue Points 1 and 4 represent Brenda or Dennis “They have the same height” Point 1 represents Dennis “He is older than Brenda” So point 4 represents Brenda “She is younger than Dennis” 7 62 5 214
  21. 21. 1. The Bus Stop Queue 7 62 5 214
  22. 22. 2. Planes A (Dusty) B (Siddeley)
  23. 23. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B
  24. 24. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive than airplane A
  25. 25. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper
  26. 26. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper
  27. 27. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper  The faster airplane is smaller
  28. 28. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper  The faster airplane is smaller
  29. 29. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper  The faster airplane is smaller  The larger airplane is older
  30. 30. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper  The faster airplane is smaller  The larger airplane is older
  31. 31. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper  The faster airplane is smaller  The larger airplane is older  The cheaper airplane carries fewer passengers
  32. 32. 2. Planes A (Dusty) B (Siddeley)  Airplane A is older than airplane B  Airplane B is more expensive tan airplane A  The older airplane is cheaper  The faster airplane is smaller  The larger airplane is older  The cheaper airplane carries fewer passengers
  33. 33. 2. Planes A (Dusty) B (Siddeley)
  34. 34. 3. Which Graph? The 100 metres race. The men's world record is 9.58 seconds, set by Usain Bolt 0,00 2,00 4,00 6,00 8,00 10,00 12,00 0 50 100 150SPEED DISTANCE GRAPH 3 0 2 4 6 8 10 12 0 50 100 150 SPEED DISTANCE GRAPH 1 0 2 4 6 8 10 12 0 50 100 150 SPEED DISTANCE GRAPH 2
  35. 35. 0,00 2,00 4,00 6,00 8,00 10,00 12,00 0 20 40 60 80 100 120 140 SPEED DISTANCE GRAPH 3 3. Which Graph?
  36. 36. To sum up… Graphsare very useful to draw conclusionsfrom different set of data and to find if there is a correlation between them. http://www.nytimes.com/interactive/2012/08/05/sports/olympics/the-100-meter-dash-one-race-every-medalist-ever.html?_r=0
  37. 37. The language of graphs Mathematics. 1st Year Secondary Education

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